{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('3.0.3', '1.16.3')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matplotlib.__version__,np.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "y = np.random.normal(size=50)\n",
    "\n",
    "plt.ylim(-3,3)\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.legend(['line plot 1'])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## multiple plots same axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "x = np.linspace(0.0,100,20)\n",
    "\n",
    "y1 = np.random.normal(scale=0.2,size=20)\n",
    "y2 = np.random.normal(scale=0.5,size=20)\n",
    "y3 = np.random.normal(scale=0.8,size=20)\n",
    "\n",
    "plt.ylim(-3,3)\n",
    "\n",
    "plt.plot(x,y1,label='plot 1')\n",
    "plt.plot(x,y2, label='plot 2')\n",
    "plt.plot(x,y3, label='plot 3')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## legend for single axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "fig, axes = plt.subplots(2,2)\n",
    "\n",
    "# just plot things on each individual axes\n",
    "x = np.linspace(0.0,100,20)\n",
    "y1 = np.random.normal(scale=0.2,size=20)\n",
    "y2 = np.random.normal(scale=0.5,size=20)\n",
    "y3 = np.random.normal(scale=0.8,size=20)\n",
    "\n",
    "axes[0][0].scatter(x,y1)\n",
    "axes[0][1].bar(x,y1,width=3.0)\n",
    "axes[1][0].scatter(x,y2)\n",
    "axes[1][1].plot(x,y2)\n",
    "\n",
    "# you can set a legend for a single subplot\n",
    "axes[1][1].legend(['plot 4'])\n",
    "\n",
    "plt.subplots_adjust(wspace=0.2, hspace=0.2)\n",
    "\n",
    "plt.gcf().set_size_inches(8,8)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## legend for scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "y = np.random.normal(size=50)\n",
    "y2 = np.random.normal(size=50)\n",
    "\n",
    "plt.ylim(-3,3)\n",
    "\n",
    "plt.scatter(x,y,label='plot 1')\n",
    "plt.scatter(x,y2,label='plot 2')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## disable legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f4xQfSx3tdlQmAlmiN6ajVR6EZXfA1hehTzpc/GcY8wVwtiobE3KW6I3pKE31sO7XsOrnoD6YfQtM/z506eF2ZCbCWaI3piNsex2W3gLluyDzPDjnp5A01O2oTJSwRG9Meyrb6RQf27YU+mbAFS/ByBy3ozJRxhK9Me2hoQZW/xz+8yuI7QLz74Gp34G4Lm5HZqKQJXpjQkkVPngJ3rgDqg46e+Hn/QR693c7MhPFLNEbEyrFH8BrN8Oe1dDvc/CVpyB9mttRGWOJ3pigHTsCKx6AjU84Nzp9/lGY/DWIiXU7MmMAS/TGtJ3fD+/+1Sk+VlsGWddA9h3QI9ntyIz5L5bojWmLA5udGvEHN8PgaXDlS9D/NLejMua4WlUxSUSeEhGviGxtMZYsIstEZHvgZ1JgXETklyKyQ0S2iMjp7RW8MR3uaAm8fB38Mdu5w/XLi+HapZbkTVhrbWm8p4EFnxi7BchV1QwgN/AcYCFOC8EMYBHwu+DDNMZlviZY/3v41WR473k463/ge5vgtEusdIEJe61aulHVVSIy9BPD5+O0GAR4BlgB3BwYfzbQMHy9iCSKSH9VLQpFwMZ0uN2rYMlNUJIPI7Kd4mMpGW5HZUyrBbNGn9YieR8G0gKPBwL7Wxx3IDBmid50LpUHnGbcH/wTEtPhkr9C5udtBm9c5fMr7+4/Ql5BcavfE5KLsaqqIqKn8h4RWYSztEN6enoowjAmNBrrYN2vYPWjoH6YcxtM/x+I7+52ZCZKVR5rZNW2EpYXeFmxrYTymgZiY1o/4Qgm0Rd/tCQjIv0Bb2D8IDC4xXGDAmP/RVUXA4sBsrKyTuk/Esa0C1WnJs3SW6BiD4z5olN8LNEmIqZjqSo7S46SV+AlN9/Lpr0V+PxKUo945o72MDfTw6xRqSQ+0LrPCybRvwJcDTwY+Plyi/HrReTvwFSg0tbnTdgr3eEk+B3LIGU0XPkvGDHX7ahMFKlv8rFhVzl5BV7yCrzsK68FILNfL749ezjZmR4mDk46pZn8R1qV6EXkOZwLrykicgC4CyfBvyAiXwf2AhcHDl8CnAvsAGqBa045KmM6Sv1RWPUzWPcbiOsGZ/8Upn4LYuPdjsxEAW9VHcsLnVn7mh2l1Db46BoXw4yRKSyaNZy5mR4GJga/ZNjaXTeXneClT9VbDey2uS6YoIxpd6pOh6c37oDqQ3DaV2He3dAr7WTvNKbN/H5ly8HKwKy9mK0HqwAY0KcbF5w+kJzMNM4c0Zdu8aEtn2F3xproc/h9p/jY3rXQfyJc/AwMnuJ2VCZCVdc1smZ7KXkFXpYXllB6tJ4YgUnpSdx4zmhyxngYndYLacfdXJboTfSoLYfl98OmJ6FbInzhcZh0pRUfMyG3p7SG3AIvywu8bNhdRqNP6dUtjtmjUskZ42H2KA/JCR3Xm8ASvYl8fh+8/Szk3gN1RyDr6zD3Nis+ZkKm0efnrT3l5OV7ySv0squkBoCRnp5cO30YczM9TB6SRHxsa4sRhJYlehPZ9m+EJTdC0buQfhac+7BTK96YIJUerWdFobO3fdW2Eqrrm+gSG8PU4clcNW0I2ZlppPcNj8bvluhNZKoudsoHv/c36NUfLnwSxl9od7WaNlNVPiyqap61v7v/CKrg6dWVz0/oT3amh+kjU0joGn5pNfwiMiYYvkbY8AdY8SA01cH0H8CsG6FrT7cjM53QsQYfa3eUNq+3H66qA+C0QX34Qc4ocsZ4GNu/NzFt2NvekSzRm8ixc7mzm6a0EEbOhwUPQspIt6Myncz+8lqWFzo3La3bWUZ9k5+eXeOYmZFCdqaHOaM9pPbq6naYp8QSven8juyD138M+a9A0lC47O8waoEt05hWafL5eXvfkea97duKjwIwtG8PLp86hJwxHs4YmkyXOHcupIaCJXrTeTUeg7W/hDWPOc+zb4czvwfx3dyNy4S9I7UNrNxWQm6+l5XbSqg81khcjDBlWDIXZw0mO9PD8NTIWe6zRG86H1Uo+H/w+q3ObH7cl+Hs+6DPILcjM2FKVdlWfLR51r55bwV+hb4JXZg3Jo2cMR5mZKTQu1tklr6wRG86l9Lt8NpNsDMPPGPh6n/DsFluR2XCUF2jj3W7ypxdMgVeDh45BsC4Ab25bu5IsjM9nDYoMewvpIaCJXrTOdRXw8qHYf3vIL4HLHgIzvgGxNpfYfOxw5V1zbP2tTvKONboo3t8LNNHpnB99kjmjvbQr0/0Le3Zb4kJb6qw5QVYdiccPQyTroCcu6FnqtuRmTDg8yvvHTjSPGv/sMgpEjYoqTsXZQ0iO9PDtOGhLxLW2ViiN+Gr6D2nV+v+9TDgdLj0bzBosttRGZdV1TWyelspuQXFrCj8uNvS5PQkblmYSXamhwxPz3YtEtbZWKI34ae2HPLuhc1PQ/dk+OKvYOIVENN5t7eZtlNVdpXWNM/a39pTTpNf6dM9njmjU8nO9DB7VCqJPTquSFhnY4nehA+/z0nuefdCXRVMWQRzboXuiW5HZjpYQ5OfjbvLyS0oJq/Ay94yp9vS6LRefGPmcHLGeJg0OJE4l4qEdTZtTvQiMhp4vsXQcOBOIBH4JlASGL9NVZe0OUITHfatd4qPHd4CQ2fCwocgbZzbUZkO5K2uY0VBCXkFXlZvL6GmwUeXuBjOGtGXb8xwKkAOSgqPImGdTZsTvaoWAhMBRCQWpwH4P3FaBz6mqo+EJEIT2aoPOxdatzwPvQfCV56CcRfYXa1RwO9XPjhURW5BMcsLvLx3oBKAfr278cWJA8nJ9HDWyL706GILD8EK1RnMAXaq6l67AGJapakBNvzO2TLpa4CZNzh/uiS4HZlpRzX1TazZUdpcAbKkuh4RmDg4kR+dPYq5mU6RMMsjoRWqRH8p8FyL59eLyFXAJuAGVa0I0feYSLDjTXjtFijb7tSkOed+6DvC7ahMO9lXVtu81r5hVzkNPj+9usYxa1RqoEhYKn17dq4iYZ2NOL28g/gAkS7AIWCcqhaLSBpQCihwL9BfVa89zvsWAYsA0tPTJ+/duzeoOEwnULHHKT5W8CokD3eqS446x+2oTIg1+vxs3lsRuHHJyw6vUyRseGoC2aM9ZAeKhLnVbSmSiMhmVc062XGhmNEvBN5W1WKAj34GgngCePV4b1LVxcBigKysrOD+a2PCW0MtrP0FrH0cJAZy7oQzr4c4m8VFivKaBlYESvuu2lZCVV0T8bHC1GF9uWxKOtmZHoal2LKcW0KR6C+jxbKNiPRX1aLA0y8DW0PwHaYzUoX8f8Prt0HlfqfD0/x7oc9AtyMzQVJVCg5XN8/a395XgSqk9OzKgvH9yM70MCMjlZ5h2G0pGgX1b0FEEoD5wLdaDD8sIhNxlm72fOI1Ey1KCp3iY7tWgGccXP0qDJvpdlQmCMcafKzbVUpuvtNt6VCl021pwqA+/E92BjljPIwf0CcqioR1NkElelWtAfp+YuzKoCIynVtdFax8CDb83tlBs/BhyPq6FR/rpA4eOUZeoI3e2h2l1Df56dEllpkZKXx/XgZzR3vw9I6+ImGdjf32mdDw+2HL32HZXVBTAqdfCTl3QUKK25GZU+DzK+/uryA3UG6g4HA1AOnJPZrX2qcOT6ZrXHQXCetsLNGb4B16xyk+dmAjDMyCrz4PA093OyrTSpW1jazcXsLyAi8rCr1U1DYSGyOcMTSJ2851ioSNSLUiYZ2ZJXrTdjVlkPsTePtZZ+Z+/m/htMus+FiYU1V2eJ1uS7kFXjbvrcDnV5ITujA3sP1xZkYqfbpHZrelaGSJ3pw6XxNs/pNTfKz+KEz7Lsy5Gbr1cTsycwJ1jT427C4nL7+YvEIv+8udbkuZ/Xrx7dnDyc5MY+LgRGLtQmpEskRvTs2etc5umuKtMGy2c7HVk+l2VOY4iqvqWB6Yta/dUUptg49u8TFMH5HCt2ePYO5oDwMSu7sdpukAluhN61QdgjfugK3/gD6D4aJnYOz5VnwsjPj9ypaDlc2z9q0HnW5LAxO7c8HpA8nJTOPMEdZtKRpZojefrake1v0GVj0C/iaYdRPM+CF0sXKx4aC6rpE120vJDVxILT3aQIzA6elJ3LRgNNmZHkan9bILqVHOEr05se3L4LWboXwnjP48nPNTSB7mdlRRb3dpTXMD7I27y2n0Kb27xTF7tIecQLelpATrtmQ+ZonefFr5Llh6G2x7DfqOhMtfhIx5bkcVtRqa/GzaU05u4MalXaU1AGR4enLt9GFkZ3qYPCTJui2ZE7JEbz7WUAtrHoW1v4TYeJj3E2dHTZzNDjta6dF6VhSWkFdQzOptpVTXN9ElNoZpI/py9VlDyc70MDjZls9M61iiN07xsQ//Ba/fDlUH4HMXw/x7oHd/tyOLGqpOt6WPioS9d+AIquDp1ZXPT+hPdqaH6SNTSLAiYaYN7G9NtPPmO71a96yGtM/BhU/AkLPcjioq1DY0sXZHGXmBphzFVfUAnDY4kR/OG0V2podxA6zbkgmeJfpodewIrHgQNi6Grr3g3Ecg61qIsa137Wl/eS3LC73k5ntZt6uMhiY/PbvGMTMjJdBtyUNqL6vTb0LLEn208fvhvb/Bm3dDTSlM/hpk3wEJfU/2TtMGTT4/b+870twAe1txoNtSSgJXThtCdqbTbalLnF1INe3HEn00ObjZKT52cBMMngqX/wMGTHQ7qohTUdPAym0l5BV4WbmthMpjjcTFCFOHJ3PJGdZtyXQ8S/TRoKY0UHzsz9DTA1/+A0y4xO5qDRFVZVvxUacBdr7TbcmvkNKzC/PHppGT6WFGRgq9ulmRMOOOoBO9iOwBqgEf0KSqWSKSDDwPDMXpMnWxqlYE+13mFPma4K0/wvL7obEGzrreubO1W2+3I+v06hp9rNtZ1rxL5uARp0jY+IG9uX7uSLLHpDFhoHVbMuEhVDP6uapa2uL5LUCuqj4oIrcEnt8cou8yrbF7tVN8zPshDJ8LCx+C1NFuR9WpFVV+3G1pzY5S6hr9dI+PZUZGCt/LHsncTA9p1m3JhKH2Wro5H5gTePwMsAJL9B2j8gC8cTt88E9ITIdL/gKZ59kyTRv4/Mp7B46Ql+9UgMwvcoqEDUrqziVZg8kek8bUYclWJMyEvVAkegXeEBEF/qCqi4E0VS0KvH4YSPvkm0RkEbAIID09PQRhRLnGOlj3K1j9KKgf5twK078P8VaG9lRU1TWyelspuQXFrCgsobymgdgYYfKQJG5d6HRbGumxbkumcwlFop+hqgdFxAMsE5GCli+qqgb+I8AnxhcDiwGysrI+9bo5BYVLYektULHbmb2fcz8kDXE7qk5BVdlVWkNeoEfqW3vKafIriT3imTMqlewxaczOSKVPD7uQajqvoBO9qh4M/PSKyD+BKUCxiPRX1SIR6Q94g/0ecxxlO50Ev/0NSBkFV7wEI3PcjirsNTT52bi73NklU+Blb1kt4HRb+uas4WRnejg9Pcm6LZmIEVSiF5EEIEZVqwOPzwbuAV4BrgYeDPx8OdhATQv1R2H1I06d+NiucPZ9MOVbVnzsM3ir61hR4OxtX729hJoGH13jYjhrRF++MdNJ7gOt25KJUMHO6NOAfwbWK+OAv6nqUhF5C3hBRL4O7AUuDvJ7DDjFx7a+6HR6qj4EEy6F+T+BXv3cjizs+P3K1kOVzdsftxyoBKB/n258adJAsjM9nDUihe5d7EKqiXxBJXpV3QWcdpzxMsDWEELp8FanCcjeNdBvAlz0NKRPdTuqsHK0vok120vJKyhmeWEJJdX1iMCkwYnceI7TbSmzn3VbMtHH7owNd8cqnBue3vojdOsD5z0Gp19txccC9pbVkJvvZXmhl/W7ymj0Kb26xTF7VCrZgW5LfXtakTAT3SzRhyu/D975M+Te4yT7rGth7o+hR7Lbkbmq0edn056K5tK+O0ucbksjUhO4pkW3pXjrtmRMM0v04ejAJljyIzj0DqSfCQsfhv4T3I7KNeU1DawodG5aWrWthOo6p9vS1OHJXBGoADmkrxUJM+ZELNGHk6Nep3zwu3+Fnv3ggifgcxdF3V2tqkp+UXXzrP2d/U63pdReXVk4vh85Y9KYYd2WjGk1+00JB75G2PgErHgAGo85d7TOutFpCBIljjXV3PL7AAANn0lEQVT4WLujlLxCp5ZMUWUdABMG9eH7ORlkZ3oYP8CKhBnTFpbo3bZrpVN8rKQARs6DBQ9CSobbUXWIAxW1LA9sf/zPzjLqm/wkdIllZkYqP5znYU5mKp5eViTMmGBZonfLkf3wxo/hw5chcQhc+hyMXhjRyzQ+v/LOvgpyAxUgCw5XA5Ce3IPLpjgNOaYOT6ZrnO0oMiaULNF3tMY6+M8vneJjAHNvh7O+B/GROXOtrG1k5fYS8vKLWbmthIpap9vSGUOT+fG5Y5ib6WFEaoLtbTemHVmi7yiqUPiaU5vmyF4Y+yWndEHiYLcjCylVZYf3KLmBJZnNeyvw+ZXkhC7MzfSQnelh1qhUelu3JWM6jCX6jlC6A5beDDvehNRMuOoVGD7b7ahCpq7Rx/pdZSwvcLZAHqhwui2N7d+b78weQfYYD6cNSrQiYca4xBJ9e6qvhlU/g3W/derCn/MATPkmxHb+2WxxVV1zHZk120s51uijW3wMM0am8J05I5g72sMAKxJmTFiwRN8eVOH9/3OKjx09DBOvgHl3OY25Oym/X9lysJK8/GJyC7x8cMjptjQwsTtfmTyI7EwPZ47oa92WjAlDluhDrWiLs11y3zoYMMlp5Tf4DLejapPqukZWby8lr8DLikIvpUcbiBGYPCSJmxaMJiczjVFp1m3JmHBniT5Uassh7z7Y/CfongRf+CVMuhJiOlfNlV0lR5uXZN7aU06jT+nTPZ7Zo1LJGeNhVkYqSQlW996YzsQSfbD8Pnj7Gci9F+qOwBnfhLm3Osm+E2ho8vPWnvLm5L671CkSNiqtJ9fOGEb2aKdIWJwVCTOm07JEH4x9G+C1G6HoPRgy3Sk+1m+821GdVEl1PSsKvYFuS6UcrXeKhJ05oi9fO2so2ZkeBif3cDtMY0yItDnRi8hg4FmcLlMKLFbVx0XkbuCbQEng0NtUdUmwgYaV6mJ48y547znoNQAufBLGXxi2d7WqKh8cqiIvsP1xywGnSFha76584bT+zB3tYboVCTMmYgXzm90E3KCqb4tIL2CziCwLvPaYqj4SfHhhxtcIG34PKx4CXz3M+F+YeQN07el2ZJ9S2+B0W1oemLkXVzndlk4blMgP540iO9PDuAG97UKqMVGgzYleVYuAosDjahHJBwaGKrCwszPPaeVXug0yzoEFD0DfEW5H9V/2l9c2z9rX7yqjoclPr65xzByVwtzRHuZmekixbkvGRJ2Q/L+6iAwFJgEbgOnA9SJyFbAJZ9ZfcZz3LAIWAaSnp4cijPZRsdcpPpb/b0gaBpc9D6MXuB0VAE0+P5v3VpBX6CUv38t271EAhqckcFWgIUfW0GS6xNmFVGOimahqcB8g0hNYCfxUVV8SkTSgFGfd/l6gv6pe+1mfkZWVpZs2bQoqjpBrPAZrH4c1j4HEOEs0Z17vevGxipoGVm4rIbfAy8pCL1V1TcTHClOGJZOdmUZ2podhKdZtyZhoICKbVTXrZMcFNaMXkXjgReCvqvoSgKoWt3j9CeDVYL6jw6lCwavw+m1wZB+MuwDOvhf6DHIpHKWwuNrZ/pjv5e19FfgVUnp24exx/cjJ9DAjI4VeViTMGHMCwey6EeBJIF9VH20x3j+wfg/wZWBrcCF2oJJtzl2tu5aDZyxc/SoMm9nhYdQ1+li3s4zcgmKWF5Rw8IhTJGz8wN5cn+10W5ow0LotGWNaJ5gZ/XTgSuB9EXk3MHYbcJmITMRZutkDfCuoCDtCXRWsfMjZUROf4OyHz/o6xHbcdsOiymPNs/a1O0upa/TTo0ss00em8L3skczN9JDWOzJr1htj2lcwu27WAMebUnaePfN+P2x53tkTf9QLk66AnLugZ2q7f7XPr7y7/0igAXYJ+UVOkbDByd25JGsw2WPSmDos2YqEGWOCFr13yBx6F5bcCAc2wsDJcNlzzs92VHmskVXbSlhe4GXFthLKaxqIjRGyhiRx68JMcsZ4GJFqRcKMMaEVfYm+pgzy7oHNz0BCCpz/Gzjtq+1SfExV2RkoEpab72VToNtSUo945gT2tc/OSKVPD7uQaoxpP9GT6P0+2PSUU2GyvhqmfQdm3wzdE0P6NfVNPjbuLic338vyQi97y2oByOzXi2/NGk7OGA8TBydZtyVjTIeJjkS/9z+w5CYofh+GznQutqaNDdnHe6vqmksNrN5eSm2Dj65xMUwfmcI3Zg4nO9PDQOu2ZIxxSWQn+qoiWHaH0+2p9yC46GmnKXeQa+B+v/L+wcrm0r7vH6wEYECfbnx50kByxng4c3gK3bvYhVRjjPsiM9E3NcD63zr9Wn2NMOtGmPFD6NL2O0aP1jexZntJILmXUHrUKRJ2enoSN54zmuxMD5n9etmFVGNM2Im8RL/9TVh6M5TtgFELYcH9kDy8TR+1t6yG3Hxn1r5hdxmNPqVXt7jmbkuzR3lItm5LxpgwFzmJvny3U7agcAkkj4DL/wEZ80/pIxp9fjbtqSCvwGmAvavE6bY0IjUh0JAjjayhScRbtyVjTCfS+RN9Q61TeGzt4xATB/PuhmnfhbjWleMtO1rPisIS8gq9rNpWQnWd021p6vBkrgxUgBzS14qEGWM6r86b6FXhw5fhjduhcj987iKYfw/0HnCStykfFlWxPFC3/d39Trel1F5dOXd8f7LHeJhh3ZaMMRGkc2Yzb4FTfGz3Skj7HFywGIacdcLDjzX4WLujlNwCLysKvRRV1gFw2qA+/CDn425LViTMGBOJOleir6t02vht/AN06QnnPgKTrzlu8bH95bXNe9v/s9PptpTQJZaZGan8cL6HOaNT8fSyImHGmMjXORK93+804n7zbqgpgclfg+w7IKFv8yFNPj/v7D8S2CVTzLZip9vS0L49uGKqs9Y+ZZh1WzLGRJ/wT/QH33aWaQ68BYOmwOUvwIBJABypdbot5RV4WVFYQuWxRuJihDOGJnP75weTnelheGr4Ne42xpiOFL6JvqYUcu+Bt5+FhFT40u/RCRezvaSW3BU7WV7gZdPecvwKfRO6MG+M00Zv5qgUelu3JWOMadZuiV5EFgCPA7HAH1X1wVa90dfkFB9bfh801NA09TusG/wNlu08Ru7Slc3dlsb27811c52GHKcNSrQiYcYYcwLtkuhFJBb4DTAfOAC8JSKvqOqHn/nGPWudGvHeDyjqO43f9l3EP/6TwLHGArrHO92WnOSeSv8+ViTMGGNao71m9FOAHaq6C0BE/g6cDxw/0fsaqHjmCpJ2/5viGA93NvyA1w+ewaCkHlyU5SE708O04X2t25IxxrRBeyX6gcD+Fs8PAFNPdLC/OJ8euw7xS98FbBx4FTPGpnNDpocMj3VbMsaYYLl2MVZEFgGLAEb378mqs/8fV02axP/0sCJhxhgTSu21qfwgMLjF80GBsWaqulhVs1Q1q+eA0cyfPpVES/LGGBNy7ZXo3wIyRGSYiHQBLgVeaafvMsYY8xnaZelGVZtE5HrgdZztlU+p6gft8V3GGGM+W7ut0avqEmBJe32+McaY1rHCL8YYE+Es0RtjTISzRG+MMRHOEr0xxkQ4S/TGGBPhRFXdjgERqQYK3Y4jzKQApW4HEUbsfPw3Ox+fFo3nZIiqpp7soHCpR1+oqlluBxFORGSTnZOP2fn4b3Y+Ps3OyYnZ0o0xxkQ4S/TGGBPhwiXRL3Y7gDBk5+S/2fn4b3Y+Ps3OyQmExcVYY4wx7SdcZvTGGGPaieuJXkQWiEihiOwQkVvcjqejichTIuIVka0txpJFZJmIbA/8THIzxo4kIoNFZLmIfCgiH4jI9wPj0XxOuonIRhF5L3BOfhIYHyYiGwK/O88HSoJHDRGJFZF3ROTVwPOoPh+fxdVE36KJ+EJgLHCZiIx1MyYXPA0s+MTYLUCuqmYAuYHn0aIJuEFVxwLTgOsCfyei+ZzUA9mqehowEVggItOAh4DHVHUkUAF83cUY3fB9IL/F82g/Hyfk9oy+uYm4qjYAHzURjxqqugoo/8Tw+cAzgcfPAF/q0KBcpKpFqvp24HE1zi/yQKL7nKiqHg08jQ/8USAb+EdgPKrOiYgMAj4P/DHwXIji83Eybif64zURH+hSLOEkTVWLAo8PA2luBuMWERkKTAI2EOXnJLBM8S7gBZYBO4EjqtoUOCTafnd+AdwE+APP+xLd5+MzuZ3ozUmosy0q6rZGiUhP4EXgB6pa1fK1aDwnqupT1Yk4/ZenAJkuh+QaETkP8KrqZrdj6SzcLoFw0ibiUapYRPqrapGI9MeZxUUNEYnHSfJ/VdWXAsNRfU4+oqpHRGQ5cCaQKCJxgVlsNP3uTAe+KCLnAt2A3sDjRO/5OCm3Z/TWRPz4XgGuDjy+GnjZxVg6VGCt9UkgX1UfbfFSNJ+TVBFJDDzuDszHuXaxHPhK4LCoOSeqequqDlLVoTg5I09VLydKz0druH7DVOC/yr/g4ybiP3U1oA4mIs8Bc3Aq7xUDdwH/Al4A0oG9wMWq+skLthFJRGYAq4H3+Xj99TacdfpoPScTcC4uxuJMzl5Q1XtEZDjOBoZk4B3gClWtdy/Sjicic4Afqep5dj5OzPVEb4wxpn25vXRjjDGmnVmiN8aYCGeJ3hhjIpwlemOMiXCW6I0xJsJZojfGmAhnid4YYyKcJXpjjIlw/x9OQcFflhbL3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "y = x*2\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'x':x,\n",
    "    'y':y\n",
    "})\n",
    "\n",
    "# this will add legends by default\n",
    "df.plot(kind='line')\n",
    "\n",
    "plt.gca().legend_.remove()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## customize number of columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "\n",
    "y2 = x*2\n",
    "y3 = x*3\n",
    "y4 = x*4\n",
    "y5 = x*5\n",
    "y6 = x*6\n",
    "y7 = x*7\n",
    "y8 = x*8\n",
    "y9 = x*9\n",
    "y10 = x*10\n",
    "\n",
    "plt.plot(x,y2,label='y=2x',linewidth=3)\n",
    "plt.plot(x,y3,label='y=3x',linewidth=3)\n",
    "plt.plot(x,y4,label='y=4x',linewidth=3)\n",
    "plt.plot(x,y5,label='y=5x',linewidth=3)\n",
    "plt.plot(x,y6,label='y=6x',linewidth=3)\n",
    "plt.plot(x,y7,label='y=7x',linewidth=3)\n",
    "plt.plot(x,y8,label='y=8x',linewidth=3)\n",
    "plt.plot(x,y9,label='y=9x',linewidth=3)\n",
    "plt.plot(x,y10,label='y=10x',linewidth=3)\n",
    "\n",
    "plt.legend(ncol=2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## legend outside of plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "\n",
    "y2 = x*2\n",
    "y3 = x*3\n",
    "y4 = x*4\n",
    "y5 = x*5\n",
    "\n",
    "\n",
    "plt.plot(x,y2,label='y=2x')\n",
    "plt.plot(x,y3,label='y=3x')\n",
    "plt.plot(x,y4,label='y=4x')\n",
    "plt.plot(x,y5,label='y=5x')\n",
    "\n",
    "plt.gca().legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
    "\n",
    "# box = plt.gca().get_position()\n",
    "# plt.gca().set_position([box.x0, box.y0, box.width * 0.8, box.height])\n",
    "\n",
    "plt.gcf().set_size_inches(6,5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sort legend labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "\n",
    "y2 = x*2\n",
    "y3 = x*3\n",
    "y4 = x*4\n",
    "y5 = x*5\n",
    "y6 = x*6\n",
    "y7 = x*7\n",
    "\n",
    "colour_blind_cycle = ['#377eb8', '#ff7f00', '#4daf4a',\n",
    "                  '#f781bf', '#a65628', '#984ea3',\n",
    "                  '#999999', '#e41a1c', '#dede00']\n",
    "\n",
    "\n",
    "plt.gca().set_prop_cycle(color=colour_blind_cycle)\n",
    "\n",
    "plt.plot(x,y2,label='y=2x',linewidth=3)\n",
    "plt.plot(x,y3,label='y=3x',linewidth=3)\n",
    "plt.plot(x,y4,label='y=4x',linewidth=3)\n",
    "plt.plot(x,y5,label='y=5x',linewidth=3)\n",
    "plt.plot(x,y6,label='y=6x',linewidth=3)\n",
    "plt.plot(x,y7,label='y=7x',linewidth=3)\n",
    "\n",
    "\n",
    "current_handles, current_labels = plt.gca().get_legend_handles_labels()\n",
    "\n",
    "reversed_handles = list(reversed(current_handles))\n",
    "reversed_labels = list(reversed(current_labels))\n",
    "\n",
    "plt.legend(reversed_handles,reversed_labels)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sort legend labels using pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "# generate random data for plotting\n",
    "x = np.linspace(0.0,100,50)\n",
    "\n",
    "y  = x*1\n",
    "y2 = x*2\n",
    "y3 = x*3\n",
    "y4 = x*4\n",
    "y5 = x*5\n",
    "y6 = x*6\n",
    "y7 = x*7\n",
    "\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'y':y,\n",
    "    'y2':y2,\n",
    "    'y3':y3,\n",
    "})\n",
    "\n",
    "# this will add legends by default\n",
    "df.plot(kind='line',legend='reverse')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
